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Home/Chain Registry/Block #3,505,266

Block #3,505,266

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/8/2020, 12:07:12 PM Β· Difficulty 10.9306 Β· 3,339,448 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
f08bcd3364753c167d70264906b5d250ee5d6dd2c8dcbdfeebd044c1aa444938
View on Chainz β†—

Difficulty

10.930637

Transactions

1

Size

199 B

Version

2

Bits

0aee3e42

Nonce

584,378,097

Timestamp

1/8/2020, 12:07:12 PM

Confirmations

3,339,448

Merkle Root

90274dca6a4dc3ad7ce5b57af961171d04d9283dfbf735a422bd5da799f4a7ad
Transactions (1)
Coinbase90274dca6a4dc3…bd5da799f4a7ad
1 in β†’ 1 out8.3600 XPM109 B
AJg1pctp…g6u8Y2w4
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.632 Γ— 10⁹⁡(96-digit number)
46329838112227902705…95931334730845868240
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
4.632 Γ— 10⁹⁡(96-digit number)
46329838112227902705…95931334730845868239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.632 Γ— 10⁹⁡(96-digit number)
46329838112227902705…95931334730845868241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
9.265 Γ— 10⁹⁡(96-digit number)
92659676224455805410…91862669461691736479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.265 Γ— 10⁹⁡(96-digit number)
92659676224455805410…91862669461691736481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.853 Γ— 10⁹⁢(97-digit number)
18531935244891161082…83725338923383472959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.853 Γ— 10⁹⁢(97-digit number)
18531935244891161082…83725338923383472961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
3.706 Γ— 10⁹⁢(97-digit number)
37063870489782322164…67450677846766945919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.706 Γ— 10⁹⁢(97-digit number)
37063870489782322164…67450677846766945921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
7.412 Γ— 10⁹⁢(97-digit number)
74127740979564644328…34901355693533891839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.412 Γ— 10⁹⁢(97-digit number)
74127740979564644328…34901355693533891841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 3505266

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock f08bcd3364753c167d70264906b5d250ee5d6dd2c8dcbdfeebd044c1aa444938

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #3,505,266 on Chainz β†—
Circulating Supply:58,002,123 XPMΒ·at block #6,844,713 Β· updates every 60s
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